Evaluate: `lim_(x -> pi/6) (cot^2 x - 3)/("cosec" x - 2)`

Given that `lim_(x -> pi/6) (cot^2 x - 3)/("cosec" x - 2)` = `lim_(x -> pi/6) ("cosec"^2 x - 1 - 3)/("cosec" x - 2)` = `lim_(x -> pi/6) ("cosec"^2x - 4)/("cosec" x - 2)` = `lim_(x -> pi/6) (("cosec" x + 2)("cosec" x - 2))/(("cosec" x - 2))` = `lim_(x -> pi/6) ("cosec" x + 2)` Taking limit we have = `"cosec" pi/6 + 2` = 2 + 2 = 4

Evaluate: coseclimx→π6cot2x-3cosec x-2 - Mathematics

Question

Evaluate: $lim_{x \to \frac{π}{6}} \frac{\cot^{2} x - 3}{cosec x - 2}$

Sum

Solution

Given that $lim_{x \to \frac{π}{6}} \frac{\cot^{2} x - 3}{cosec x - 2}$

= $lim_{x \to \frac{π}{6}} \frac{{cosec}^{2} x - 1 - 3}{cosec x - 2}$

= $lim_{x \to \frac{π}{6}} \frac{{cosec}^{2} x - 4}{cosec x - 2}$

= $lim_{x \to \frac{π}{6}} \frac{(cosec x + 2) (cosec x - 2)}{(cosec x - 2)}$

= $lim_{x \to \frac{π}{6}} (cosec x + 2)$

Taking limit we have

= $cosec \frac{π}{6} + 2$

= 2 + 2

= 4

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Limits of Trigonometric Functions

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Q 25 Q 24 Q 26

Chapter 13: Limits and Derivatives - Exercise [Page 240]

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Evaluate: coseclimx→π6cot2x-3cosec x-2 - Mathematics

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